Quantitative Aptitude

Clocks and Calendars

428 Questions
All Angle between hands 150 Clock gaining or losing time 132 Clock hands coincidence 69 Right angle times 30 Find time from angle 21 Decoding mixed date formats 7 Find day using reference date 6 Repeating same calendar 6 Date without reference day 3

Clocks and Calendars Questions

Multiple choice

Out of the following, Which statements are correct? (i) two plane mirrors are inclined to each other at an angle of $ 60^0 $ , if a ray of light incident on the first mirror is parallel to the second mirror, it is reflected from the second mirror parallel to the first mirror. (ii) A bird flying high up in the air does not cast a shadow on the ground because layers of atmosphere are dense (iii) if a ray reflected successively from two plane mirrors inclined at a certain angle undergoes a deviation of $ 300^0 $, then the number of images observable is 11 (iv) A clock indicates a time of 3:25 . on seeing it in a plane mirror, the time appears as 8:35

  1. (i) and (iv)

  2. (ii) and (iii)

  3. (i), (ii) and (iv)

  4. (i), (iii) 
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

A thermostated chamber at a height h above earth's surface and maintained at $30^{\mathrm{o}}\mathrm{C}$ has a clock fitted with an uncompensated pendulum. The maker of the clock has wrongly designed it to maintain correct time at $20^{\mathrm{o}}\mathrm{C}$. It is found that if the chamber is brought to earth's surface the clock clicks correct time. $\mathrm{R}$ is the radius of earth. What is the linear compressibility of the material of the pendulum?
  1. $\displaystyle \frac{\mathrm{h}}{10\mathrm{R}}$
  2. $\displaystyle \frac{5\mathrm{R}}{h}$
  3. $\displaystyle \frac{\mathrm{h}}{5\mathrm{R}}$
  4. $\displaystyle \frac{\mathrm{h}}{20\mathrm{R}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The time period of a pendulum is T = 2*pi*sqrt(L/g). The change in length due to temperature is dL = L*alpha*dT, and the change in g due to height is dg = -2*g*h/R. For the clock to keep correct time, the fractional change in length must balance the fractional change in gravity, leading to alpha*dT = h/R, where dT = 10 degrees. Thus, alpha = h/(10R).

Multiple choice

The measure of an angle in degrees, grades and radians be D, G and C respectively, then relation between them $\displaystyle \frac{D}{90}=\frac{G}{100}=\frac{2C}{\pi }$ but $\displaystyle 1^{\circ}=\left ( \frac{180}{\pi } \right )^{\circ}:\simeq 57^{\circ},17',44.{8}''$ and sum of interior angles of a $n$-sided regular polygon is $\displaystyle \left ( 2n-4 \right )\dfrac {\pi }2$. On the basis of above information, answer the following questions : The angles between the hour hand and minute hand of a clock at half past three is -
  1. $\displaystyle \frac{\pi }{3}$
  2. $\displaystyle \frac{\pi }{4}$
  3. $\displaystyle \frac{5\pi }{12}$
  4. $\displaystyle \frac{7\pi }{12}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At 3:30, the minute hand is at 180 degrees and the hour hand is at 105 degrees. Their smaller angle is 75 degrees, which equals 75 × pi/180 = 5pi/12 radians. Therefore, option C is correct.

Multiple choice

An accurate pendulum clock is mounted on the ground floor of high building. How much time will it lose or gain in one day if it is transferred to top storey of a building which is h = 200m higher than the ground floor. Radius of earth is 6.4 × 106m.

  1. it will lose 6.2s

  2. it will lose 2.7s

  3. it will gain 5.2s

  4. it will gain 1.6s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The time period of a pendulum is inversely proportional to the square root of the acceleration due to gravity, g. At a height h, the gravity is reduced to g' = g(1 - 2h/R), which increases the time period by a fraction of h/R. Thus, the clock runs slower and loses time equal to 86400 * (h/R) = 86400 * 200 / (6.4 * 10^6) = 2.7 seconds per day.

Multiple choice

A watch was set accurately at 8:30 am and then lost 2 seconds every 5 minutes. What is the time that would be indicated by the watch at 6:30 pm on the same day?

  1. 5:56

  2. 6:00

  3. 6:23

  4. 6:26

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The time elapsed from 8:30 am to 6:30 pm is 10 hours, which is 600 minutes. Since the watch loses 2 seconds every 5 minutes, it loses (600 / 5) * 2 = 240 seconds, which equals 4 minutes. Therefore, the watch will show 6:26 pm.

Multiple choice

A clock is set right at 10 p.m. The clock gains 20 minutes in 12 hours. What will be the right time when the clock indicates 10 a.m. on the following day?

  1. 9:39 a.m.

  2. 9:41 a.m.

  3. 10:21 a.m.

  4. 10:19 a.m.

  5. 9:31 a.m.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The clock gains 20 minutes in 12 hours. This means for every 720 minutes of real time, the clock shows 740 minutes. The clock shows 10 a.m. the next day, which is 12 hours later. The ratio of real time to clock time is 720/740. Real time passed = 12 * (720/740) = 11 hours and 40.5 minutes. 10 p.m. + 11h 40.5m = 9:40.5 a.m.